PMID: 11308983Apr 20, 2001Paper

Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation: large-scale behavior of the turbulent transport coefficient

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
A V Milovanov

Abstract

The formulation of the fractional Fokker-Planck-Kolmogorov (FPK) equation [Physica D 76, 110 (1994)] has led to important advances in the description of the stochastic dynamics of Hamiltonian systems. Here, the long-time behavior of the basic transport processes obeying the fractional FPK equation is analyzed. A derivation of the large-scale turbulent transport coefficient for a Hamiltonian system with 11 / 2 degrees of freedom is proposed in connection with the fractal structure of the particle chaotic trajectories. The principal transport regimes (i.e., a diffusion-type process, ballistic motion, subdiffusion in the limit of the frozen Hamiltonian, and behavior associated with self-organized criticality) are obtained as partial cases of the generalized transport law. A comparison with recent numerical and experimental studies is given.

References

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Feb 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G Zimbardo, P Veltri
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Oct 25, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G ZimbardoP Pommois
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A V Milovanov, G Zimbardo

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Citations

Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A V Milovanov, L M Zelenyi
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P PommoisG Zimbardo
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander V Milovanov
Jul 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander V Milovanov, Alexander Iomin
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A ShalchiG P Zank

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